Zero-inflated log normal distribution

Density, distribution function, and random generation for the zero-inflated log normal distribution.

Usage

dzilnorm(x, meanlog = 0, sdlog = 1, zeroprob = 0, log = FALSE)

pzilnorm(q, meanlog = 0, sdlog = 1, zeroprob = 0,
         lower.tail = TRUE, log.p = FALSE)

rzilnorm(n, meanlog = 0, sdlog = 1, zeroprob = 0)

plnorm(q, meanlog = 0, sdlog = 1, lower.tail = TRUE, log.p = FALSE)

Arguments

x, q

vector of quantiles

meanlog, sdlog

mean and standard deviation of the distribution on the log scale with default values of 0 and 1 respectively.

zeroprob

zero-inflation probability between 0 and 1.

log, log.p

logical; if TRUE, probabilities/ densities \(p\) are returned as \(\log(p)\).

lower.tail

logical; if TRUE, probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

n

number of random values to return

Value

dzilnorm gives the density, pzilnorm gives the distribution function, and rzilnorm generates random deviates.

Details

This implementation allows for automatic differentiation with RTMB.

$$f(x;\,\mu_{\ell},\sigma_\ell,p_0) = p_0\,\mathbf{1}[x=0] + (1-p_0)\,f_{\mathrm{LN}}(x;\,\mu_\ell,\sigma_\ell)\,\mathbf{1}[x>0],$$ where \(p_0\) is zeroprob, \(\mu_\ell\) = meanlog, \(\sigma_\ell\) = sdlog, and \(f_{\mathrm{LN}}\) is the log-normal density.

Examples

x <- rzilnorm(1, 1, 1, 0.5)
d <- dzilnorm(x, 1, 1, 0.5)
p <- pzilnorm(x, 1, 1, 0.5)